Question

A fraction become 1/3 when 1 is subtracted from the numerator and it become 1/4 when 8 is added to it's denominator. Find the fraction.​

Answer 1

Given :

A fraction become 1/3 when 1 is subtracted from the numerator and it become 1/4 when 8 is added to it's denominator.

To find :

• The fraction

Solution :

• Let the required fraction be x/y

A fraction become 1/3 when 1 is subtracted from the numerator

→ x - 1/y = ⅓

→ 3(x - 1) = y

→ 3x - 3 = y

→ 3x - y = 3 ----(i)

It become 1/4 when 8 is added to it's denominator.

→ x/y + 8 = ¼

→ 4x = y + 8

→ 4x - y = 8 -----(ii)

Subtract both the equations

→ 3x - y - (4x - y) = 3 - 8

→ 3x - y - 4x + y = - 5

→ - x = - 5

→ x = 5

Put the value of x in eqⁿ (ii)

→ 4x - y = 8

→ 4 × 5 - y = 8

→ 20 - y = 8

→ y = 20 - 8

→ y = 12

•°• Required fraction = x/y = 5/12

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Answer 2

$\huge \bf Required\: Answer$

Let the fraction be x/y

x - 1/y = ⅓

3(x - 1) = y

3x - 3 = y

3x - y = (3) (Eq 1)

Now,

When 8 added to denominator

x/y + 8 = ¼

4x = y + 8

4x - y = 8(Eq 2)

3x - y (4x - y) = 3 - 8

3x - y (4x - y) = -5

3x - 4x (y - y) =- 5

-x = -5

x = 5

Now,

Finding y

4x - 8 = y

4(5) - 8 = y

20 - 8 = y

12 = y

Hence :-

$\large \sf Fraction \: = \dfrac{5}{12}$